Transcript Lecture Three (Powerpoint format)

Science 3210 001 : Introduction to Astronomy
Lecture 3 : Planetary Orbits, Physics of Motion,
Matter, and Light
Robert Fisher
Items
 Course Webpage -- New Homework
 Questions
 Far Out Friday at Adler Planetarium -- March 9, 2008
Review of Lecture 1
 Astronomy is an ancient subject, passed down from Greek to
Islamic scholars, and transmitted back to the west.
 Our systems of thought evolve with time at an almost
imperceptibly slow pace, and continue to do so today.
 The universe is thought to have begun with a big bang, and is
expanding.
 The cosmic calendar varies over fantastically-long timescales.
We are very recent newcomers onto the cosmic scene.
 We are all stardust.
Review of Lecture 2
 The motion of the night sky can be described by an idealized
celestial sphere which rotates about the Earth once per day.
 The moon revolves around the Earth once per month.
 The sun appears to move inclined with respect to the distant stars
due to the earth’s tilt, by 23 degrees.
 The motion of the planets is more complex -- they appear to
wander against the distant stars, and may even appear to stop
and move backwards in an effect known as retrograde motion.
Today’s Lecture
 I) Planetary Motion
 A) Tycho Brahe
 B) Kepler and Kepler’s Laws
 II) Physics of Motion
 A) Galileo and the Physics of Kinematics
 B) Newton and Newton’s Laws of Motion
 II) Physics of Matter and Light
Planetary Motion
Tycho Brahe (1546 - 1601)
 Tycho Brahe conducted the most accurate measurements of the
stars, planets, and comets in the pre-telescopic era
 In 1572, while still a young astronomer, something absolutely
wonderful happened…
Tycho Supernova Remnant (1572) Imaged by
Chandra Space Observatory in X-Rays in 2005
Computer Simulation of an Exploding Star
Kepler Supernova Remnant (1602) Imaged by
Chandra Space Observatory in X-Rays in 2006
Johannes Kepler (1571 - 1630)
 Kepler was a talented mathematician and astronomer and contemporary
of Galileo. Hired by Tycho as an assistant, he inherited Tycho’s
observations upon his death and used them to formulate his laws of
planetary motion.
 “For if I thought the eight minutes in longitude were unimportant, I could make a
sufficient correction… Now, because they could not be disregarded, these eight
minutes alone will lead us along a path to the reform of the whole of Astronomy,
and they are the matter for a great part of this work.” -- Kepler
Kepler’s Platonic Solids Model of the Solar
System
 Kepler constructed a geometric model of the solar system, based
on the fact that there exist precisely five regular, platonic solids.
 Ancient Pythagorean idea that the planets created a music of
their own -- the “harmony of the spheres” -- that only Pythagoras
himself could hear
Kepler’s Platonic Solids Model of the Solar
System
 Circumscribing each of the five solids with a sphere, Kepler
created a model with six concentric spheres. Each of these six
spheres coincided with the orbit of one of the known planets.
Kepler’s Geometric Model of the Solar System
 Kepler’s ideas based on the harmony of the spheres may appear
as a quaint idea to us today
 This illustrates the great difficulty which the earliest scientists had
in separating their nascent scientific ideas from ancient prescientific ones
 Despite this, the apparent success of his geometric model
helped inspire and motivate him through the long difficult work
(nearly 30 years!!) that was required to analyze Tycho Brahe’s
data for the planetary orbits
Kepler’s First Law of Planetary Motion
 Kepler noted that the orbit of Mars was well-fit by an ellipse.
 His first law of planetary motion states that all planets move in elliptical
orbits, with the sun at one focus.
 He conjectured that the same law applied to the other planets as well.
Ellipses are Conic Sections
Kepler’s First Law of Planetary Motion
 The amount by which an ellipse differs from a circle is
characterized by its eccentricity -- ranging from zero for an exact
circle, to 1 to a highly elongated ellipse.
Kepler’s First Law of Planetary Motion
 All of Kepler’s laws are essentially empirical -- they describe the
properties of planetary orbits extremely well, but do not explain
why they have these particular sets of properties
 The first principles which explain Kepler’s laws were only
uncovered by Newton much later
Kepler’s Second Law of Planetary Motion
 Kepler noted that when further from the sun, Mars appeared to
move more slowly than when closer to the sun.
 He quantified this effect by his second law : planetary orbits
sweep out equal areas in equal times.
Modern Interpretation of Kepler’s Second Law
 Kepler’s second law is a direct consequence of the conservation
of angular momentum.
 If we imagine a ballerina moving her arms inward while spinning
on a frictionless ice surface, she will tend to spin faster and faster.
 Similarly, as a planet moves in closer to the sun, it will rotate
more quickly than when further out.
Kepler’s Third Law of Planetary Motion
 According to Kepler’s Second Law, the further a single planet is
from the sun, the slower it moves in its orbit.
 Kepler’s third law (sometimes referred to as his “Harmonic Law”)
states that the square of a planet’s period P (in years) is equal to
the cube of its semi-major axis a (in astronomical units).
 Mathematically, Kepler’s Third Law states P2 = a3
 Kepler thought of this law as a realization of the ancient
Pythogorean vision of the “Harmony of the Spheres”
Musical Realization of the Harmony of the
Spheres
 “Upon each of its circles stood a siren who was carried around its
movements, uttering the concords of a single scale.” -- Plato
 Jazz musician and Yale professor Willie Ruff collaborated with geologist
John Rodgers to produce a realization of the music of the spheres.
 The actual period of Pluto’s orbit is 248 years, so the actual length of a
single “track” of the music of the spheres is far greater than a human
lifespan.
 Ruff and Rodgers contracted the duration of Pluto’s orbit to about 20
minutes in duration, which also upshifted the frequencies of the inner
planets to audible frequencies.
 The outer three planets remained beneath the range of audible tones -they are played with rhythms rather than musical tones.
Galileo Galilei (1564 - 1642)
 The quantitative description of motion is the study of kinematics
 Physics as we know it today began with Galileo’s experiments of
the motion of falling bodies, which he recounted in perhaps the
first popular science book ever -- Two New Sciences
The Aristotelean World View
 Aristotle held that the speed of a falling object was directly
proportional to weight -- a heavier body falls faster than a lighter
body
 This view was colored by the influence of atmospheric friction
(imagine a rock and a feather), but even as a description of such
motions, he did not get it quite right -- the atmospheric friction
exerted on a body depends not on a body’s weight, but rather on
its surface area
 The ancient Greeks were brilliant geometers and logicians, but
still lacked the conceptual machinery to create natural laws of
motion which include both cause and effect -- this would have to
wait until Sir Isaac Newton in the 17th century
The Two New Sciences
 Two New Sciences reveals the flourishing of science, both in the
serious questioning of Aristotelean beliefs by experiment, and in
establishing new principles to take their place. Galileo describes
these developments in a dialogue between three characters :
Sagriedo, Simplicio, and Salviati.
 Sagriedo : “I greatly doubt that Aristotle ever tested by
experiment whether it be true that two stones, one weighing
ten times as much as the other, if allowed to fall, at the same
instant, from a height of, say, 100 cubits, would so differ in
speed that when the heavier had reached the ground, the
other would not have fallen more than 10 cubits.”
The Two New Sciences
 “Simplicio : His language would seem to indicate that he had tried the
experiment, because he says: We see the heavier; now the word see
shows he had made the experiment.
 Sagriedo : But I, Simplicio, who have made the test, can assure you that
a cannon ball weighing one or two hundred pounds, or even more, will
not reach the ground by as much as a span ahead of a musket ball
weighing only half a pound, provided both are dropped from a height of
200 cubits.”
An Aside on Idealizations
 Physicists use many idealizations when thinking about nature -frictionless surfaces, perfect spheres…
 While these idealizations do not exist in nature, they provide a
first approximation to the real world around us.
 Even more importantly, they provide a way of extracting what is
essential in a problem from what is not, and allow us to arrive at
general conclusions to the fundamental principles of how the
world works.
Spherical Cow Jokes…
Galileo’s Experiments on Motion
 Galileo conceived of a series of experiments which allowed him to
determine the basic physics of motion
Galileo’s Experiments on Motion
 The genius of this construction allowed him to realize that, in the
absence of friction and external forces, a moving body will
continue to move in the same direction and with the same speed
Frame of Reference
 Galileo also was perhaps the first scientist to clearly elucidate
why it can be that the Earth is moving around the sun, and yet we
do not feel the effects of its motion.
 Consider the effect of dropping a ball from the highest mast on
board a tall sailing ship -- from the standpoint of someone on the
ship, will it fall vertically, or hit the deck towards the aft side?
Galileo Movie
QuickTime™ and a
MPEG-4 Video decompressor
are needed to see this picture.
Conservation Laws
 With this series of experiments, Galileo uncovered one of the first
fundamental principles of physics -- that the motion of a body
(what we would call momentum today) remains constant in time
 These conservation laws are in a sense “The Constitution” of
physics; as new discoveries are made, their meaning is expanded
and amended, but the fundamental principles remain same
Conservation Laws
 Conservation of Momentum. The net total momentum of a
closed system is conserved in the absence of external forces.
 Conservation of Energy. The total energy of a closed system is
conserved.
 Conservation of Angular Momentum. The total amount of
rotation, or angular momentum, of a system, in the absence of
external torques is conserved.
 Conservation of Mass. The sum total of the mass in the system
is conserved… nearly so. In everyday life, this is almost exactly
true, but nuclear interactions can change the total mass of a
system slightly.
A Few Entries in the Dictionary of Physics
 The amount of matter in a body is measured by its mass. This
amount is an intrinsic property of that body, and is the same no
matter where it is measured.
 The force exerted on a body by gravity is its weight. A body’s
weight will depend on where it is measured -- a kilogram of
feathers has more weight on Earth than it does on the moon.
A Few More Entries in the Dictionary of Physics
 The motion of a body is specified by its velocity.
 Velocity has both a direction and a magnitude. For instance, a car
may be traveling 60 miles per hour in an eastwards direction.
 The magnitude of the velocity of a moving body is its speed. The
speed of the car in the previous example is 60 miles per hour.
 The rate of change of velocity of a body is its acceleration.
Example : Circular Motion
Isaac Newton (1643 - 1747)
 The discoveries of Tycho, Kepler, and Galileo culminated in the
work of Isaac Newton
 “If I have seen a little further, it is by standing on the shoulders of
giants.” -- Newton in a letter to fellow scientist Hooke
 Newton is in a sense the “architect” of physics -- he laid down the
fundamental principles of classical physics in his Principia, using
an elegant exposition inspired by Euclid’s Elements
A Page from Newton’s Principia
“I first constructed proofs for myself and then I compared my proofs with those of Newton.
The experience was a sobering one. Each time I was left with sheer wonder at the
elegance, the careful arrangement, the imperial style, and incredible originality…each
time, I felt like a schoolboy admonished by his Master.” -- Subramanyan Chandrasekhar
on Newton’s Principia
The Darker Side of Isaac Newton
 Newton was a highly complex individual -- besides his
fundamental work on motion and optics, he also pursued
extensive research in alchemy and bible studies.
 As President of the Royal Society, he has the Royal Astronomer
Flamsteed’s star catalog seized and published against his will.
 Later in life, Newton became head of the British Mint, and
personally carried out investigations against counterfeiters -including ten who were convicted and sentenced to death. He
profited enormously from this position, and died a very wealthy
man.
 Newton’s body was discovered to have been contaminated by
mercury poisoning -- most likely from his alchemical studies.
Newton’s First Law of Motion
 Newton’s first law of motion states that a body in motion will
remain in motion, unless acted upon by an outside force.
 This provides, in a nutshell, the key concept in Newton’s
framework -- that a force is tied to a change in the velocity of a
body -- an acceleration.
 A body in uniform motion experiences no net force.
 An accelerated body must experience a net force.
Newton’s First Law Example -- The Centripetal
Force
 An accelerated body must experience a net force. For circular
motion, this force is called the “centripetal force”.
Change in Velocity
Velocity
Direction of Force
Conceptual Question
Imagine that the force of gravity were to be suddenly turned off.
Would the Earth
 A) Fly off in uniform motion tangential to its orbit.
 B) Continue to orbit the sun in its current orbit.
 C) Spiral inwards towards the center of the sun.
 D) Fall directly inwards towards the sun.
Newton’s Second Law of Motion
 Newton’s second law of motion states that the force acting upon a
body is the product of the body’s mass and its acceleration -F = ma
 This is the most powerful of Newton’s three laws -- if one knows
the force acting on a body of a given mass, one can predict the
acceleration of the body and therefore the path of its motion
Newton’s Third Law of Motion
 Newton’s Third Law of Motion states that for every action, there
is an equal and opposite reaction
Conceptual Question
 Imagine that you are an astronaut on a space walk, and your jet
pack has run out. You take your jet pack off. How can you use it
to get back to the shuttle?
 A) Throw it towards the shuttle.
 B) Throw it away from the shuttle.
Newton’s Universal Law of Gravity
 Newton realized that gravity was a universal force acting both on
Earth and throughout the cosmos.
 His universal law of gravity states that the gravitational force
exerted on a test mass by a central body is directly
proportional to both the mass of the test body and the mass
of the central body, and inversely proportional to the square
of the distance between them :
F = G M1 M2 / r2
Conceptual Question
 Imagine that the sun were suddenly and instanteously replaced
by an extremely dense black hole of the same mass as the sun,
and that we can neglect any radiation or other effects other than
gravity.Would the Earth’s orbit :
 A) Expand slowly
 B) Contract slowly
 C) Remain unchanged
 D) Be swallowed by the sun
The Path of Modern Physics
 Newton’s second law exposes the fundamental questions that
have occupied physics since the time of Newton -F=ma
 What are the fundamental forces? What laws govern them?
 What are the fundamental types of matter?
Light and Matter
Physics of Waves
 Energy which comes in the form of waves (water waves, sound
waves, light waves…) can interfere with one another, producing
either larger or smaller waves.
 Interference is a unique fingerprint of wave phenomena.
Is Light a Wave?
 From the time of Newton to the 19th century, scientists debated
the nature of light -- Newton advanced a corpuscular theory of
light based on discrete particles, while others advanced a theory
of light based on waves.
 The corpuscular theory offered a simple explanation for the
reflection of light.
Is Light a Wave?
 In the 17th and 18th centuries, however, scientists discovered
effects which could not be satisfactorily explained by the
corpuscular theory.
 When passed through two narrow slits very close together, light
can be seen to form an image consisting of light and dark bands - similar to water waves passing through a breaker.
Is Light a Wave? Yes, and No!
 However, 20th century physicists have discovered that light has
particle-like properties as well -- individual atoms emit discrete
packets of light energy known as photons, similar to the idea of
Newton’s corpuscles. Einstein in fact won his Nobel prize on his
explanation of the photoelectric effect, which relied on the
photon theory of light.
 In a sense, light is both a particle and a wave. Viewed on a very
tiny scale, it is composed of discrete photons. When enormous
numbers of those photons come together, they exhibit wavelike
properties.
 The age-old question is perhaps so confusing because it is
framed in terms of something light is not -- it is a bit akin to asking
a question like, “Can computers think?”
Electromagnetic Spectrum
Spectroscopy -- Continuous Emission
 One of the most important tools modern astronomers have is the
usage of the spectrum of light detected on Earth to learn about
distant bodies.
 A single hot source of light from a solid body emits a continuous
spectrum of light energy -- blackbody radiation. The hotter the
body, the more towards the blue the spectrum will be shifted.
Spectroscopy -- Emission Lines
 When a cold cloud of gas emits light energy, it does so at a set of
unique wavelengths which are a kind of fingerprint.
Spectroscopy -- Absorption Lines
 When continuous spectrum of light energy passes through the
dark cloud, light energy is absorbed at precisely the same
wavelengths, resulting in an absorption spectrum.
Structure of Matter
 Atomic hypothesis is ancient, and dates back to at least the time
of Democritus (470 - 380 BC). Still, by 1900, the evidence for the
“reality” of atoms was sparse, and the idea was not universally
accepted.
 In early 20th century, physicists made rapid progress on atomic
structure, and discovered amazing properties of the structure of
matter on small scales.
Yummy Atomic Theory -The Plum Pudding Model of the Atom

By the early 20th century, the basic
building blocks of matter had been
discovered -- electrons, protons, and
neutrons.

Electrons carry a negative charge. They
are 2000 times lighter than protons and
neutrons and have no measurable spatial
extent.

Protons carry a positive charge. They
have a measurable spatial extent of about
a tenth of a billionth of a meter.

Neutrons are almost exactly as massive
as protons, but carry no charge. They
were not discovered until the 1920s.

Each atom consists of both electrons and
protons, and neutrons.

On average, matter must be neutral, and
so an equal number of protons and
electrons must reside in every atom.
Rutherford Experiment
 About 1910, Ernest Rutherford
devised an experiment to infer the
structure of the atom.
 Alpha particles -- what we now know
to be two protons and two neutrons - were shot into a gold foil.
 Rutherford and his assistants
measured where the alpha particle
wound up.
 Much to their surprise, they found
some alpha particles recoiled and
shot back toward the source.
 Rutherford later said, “It was quite
the most incredible event that ever
happened to me in my life. It was
almost as incredible as if you fired a
15-inch shell at a piece of tissue
paper and it came back and hit you.”
Most of the Space in the Atom is “Empty”
Helium Atom
A Note on Atomic Terminology
 The atomic number for an element is the number of protons in the
nucleus of the atom and is sometimes referred to as “Z”.
 Hydrogen Z = 1
 Helium Z = 2
 Iron Z = 26
 Because each proton carries a single unit of positive charge and the
atom as a whole must be neutral, the atomic number is also equal to the
number of electrons in a neutral atom.
 The atomic mass number for an element is the number of protons in
the nucleus plus the number of neutrons -- sometimes “A”. This varies
depending on the species, or isotope.
 Hydrogen A = 2 - 3, depending on isotope
 Carbon A 12, 13, 14, depending on isotope
The Strange World of Quantum Mechanics
 As physicists began to unravel the structure of the atom, its rules
became clearly different than the rules governing physics on much larger
scales.
 On such small scales, matter had wavelike properties. When a beam of
electrons was squeezed through a diffraction grating, it interfered with
itself, just like light.
 No matter how hard one tried to pin down the precise position and
velocity of the electron, it is impossible to specify both simultaneously.
 Perhaps most strangely of all, the rules of physics on small scales
proved to be inherently non-deterministic. This was too much for some
physicists to accept -- Einstein said, “God does not play dice with world.”
 In a cloy rebuttal, Niels Bohr replied, “Einstein, do not tell God what to do
with his dice.”
Quantum Transition
 Electrons in the atom make “quantum jumps” between one orbital and another,
and in so doing either emit or absorb a discrete packet of energy.
Quantum Transitions
 These quantum transitions
explain the spectral features of
light.
 Each line we see in a spectrum
is the unique signature of an
electron hopping between two
energy orbitals and emitting a
photon of a characteristic color.
 We can use this spectrum as a
“fingerprint” to identify the atom
which emitted it.
Next Week
 Next week we will apply these principles of planetary motion and
the nature of light to our sun and the inner bodies in the solar
system -- Mercury, Venus, Earth, and Mars.
 We will learn why Venus is too hot to sustain life today, Mars is
too cold, and Earth is just right.